$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x - 8$ and $ BC = 3x - 3$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x - 8} = {3x - 3}$ Solve for $x$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({5}) - 8$ $ BC = 3({5}) - 3$ $ AB = 20 - 8$ $ BC = 15 - 3$ $ AB = 12$ $ BC = 12$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {12} + {12}$ $ AC = 24$